Topeka (ap) — Although Kansas Sen. Pat Roberts looked vulnerable after winning his Republican primary race last week with only 48 percent of the vote, he still has an easier path to victory in November than his remaining opponents.

Democrat Chad Taylor must hold his party’s smaller base and build on it with GOP moderates and unaffiliated voters. Independent candidate Greg Orman must supplant Taylor as Roberts’ main rival and capture the support of centrists of all stripes. Both are trying to tap the same frustration with Washington and an anti-incumbent mood.

Roberts’ simpler task is to unify the GOP enough to keep his percentage of the vote in the low-to-mid 40s — and 44 percent of the state’s registered voters are Republicans. What’s more, criticism of President Barack Obama and fellow Democrats is the meat in his bloc’s diet, and Roberts began the fall campaign by throwing out raw, red chunks of it.

“The choice is pretty clear — a Republican majority in the Senate, working alongside with the House Republicans, to come up with better answers for the American people — Kansas values, Kansas ideas, not President Obama’s,” Roberts told GOP activists during a brief post-primary rally in Topeka.

Roberts, 78, is seeking his fourth, six-year term. His main primary challenger, Milton Wolf, a 43-year-old Leawood radiologist with tea-party backing, waged an aggressive campaign and garnered 41 percent of the vote with two lesser-known candidates also on the ballot.

Wolf attacked Roberts relentlessly both for his longevity and for listing rented space in the Dodge City home of two supporters as his official residence. Both issues are likely to linger during the fall campaign.

Taylor, 40, is the Shawnee County district attorney. Orman, 44, is an Olathe businessman who cofounded a business capital and management services firm. Both see voters as tired of career politicians in Washington.

“We need to send people there who are problem solvers, who want to solve problems for Americans, not position for partisan advantage,” Orman said last week.

Both Taylor and Orman pitch themselves to voters as independent centrists. Roberts has aligned himself with tea party favorite and Texas Sen. Ted Cruz — so much so that Wolf mocked him as being on “Cruz control” — and has the backing of gun-rights and anti-abortion groups.

Orman describes himself as a “pragmatic problem solver,” while Taylor spokesman Brandon Naylor called his candidate “the reasonable moderate alternative.”

“If we want to really be worried about anyone walking in lockstep with party leadership, we should take a gander at Pat Roberts,” Naylor said.

But Republicans enjoy a nearly 20-percentage point advantage in voter registration, and the GOP has won every U.S. Senate race in Kansas since 1932.

Roberts’ biggest problems in the GOP primary were to his right, with national tea party groups backing Wolf. Several GOP primary voters said they supported Wolf because they thought the younger man would be more vigorous in fighting the president — meaning they didn’t want bipartisanship.

Furthermore, Kansas Republicans have prospered by making Obama their foil. He received only 38 percent of the vote in Kansas in seeking re-election two years ago.

Republican Gov. Sam Brownback’s re-election campaign frequently links Democratic challenger Paul Davis to Obama, and U.S. Rep. Lynn Jenkins is doing the same in the 2nd Congressional District of eastern Kansas with her Democratic foe, Margie Wakefield.

Obama will shadow Taylor’s bid for the U.S. Senate because, however much he’d break with Democratic leaders, his election would make it harder for the GOP to win a Senate majority and thwart the president.

Orman contributed in 2010 to Massachusetts Republican Scott Brown’s campaign for the U.S. Senate — but after he donated larger sums in 2007 to Obama’s first presidential campaign and to his Democratic rival, Hillary Clinton.

Since then, he’s been far more generous in giving to centrist causes — more than $288,000 alone to the nonprofit Common Sense Coalition he helped found. But any past donation to Obama or Clinton makes a candidate anathema to some GOP voters.

Also, Orman said that if he is elected as an independent, he’d caucus with either party if it had a majority, something that already raises doubts for some committed Republicans.

Taylor and Orman’s first mutual problem is that many Republican voters are hungry for a GOP majority in the Senate to stymie the term-limited president during his last two years in office. In that sense, Roberts may be the safest choice for anti-Obama voters.

But Roberts’ challengers face a bigger challenge: They’re courting the same voters. Even if a majority doesn’t want or is disinterested in GOP control of the Senate, a near-even split of their votes would probably take them both down.